bash-3.2$ maude lambda.maude 
		     \||||||||||||||||||/
		   --- Welcome to Maude ---
		     /||||||||||||||||||\
	    Maude 2.5 built: May  7 2010 18:28:32
	    Copyright 1997-2010 SRI International
		   Tue Mar  8 17:54:06 2011
==========================================
rewrite in SUBSTITUTION : (/\ x . /\ y . x y z)[x / z] .
rewrites: 57 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: /\ 'var0 . /\ y . 'var0 y x
==========================================
rewrite in SUBSTITUTION : (/\ u . /\ x . /\ y . x y z)[x / z] .
rewrites: 67 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: /\ u . /\ 'var0 . /\ y . 'var0 y x
==========================================
rewrite in SUBSTITUTION : ((/\ x . x z) (/\ x . /\ y . x y z))[x / z] .
rewrites: 84 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: (/\ 'var0 . 'var0 x) (/\ 'var1 . /\ y . 'var1 y x)
==========================================
rewrite in COMBINATORY-LOGIC : S K K x .
rewrites: 2 in 0ms cpu (0ms real) (~ rewrites/second)
result Var: x
==========================================
rewrite in COMBINATORY-LOGIC : S K K (S K K) .
rewrites: 2 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S K K
==========================================
rewrite in DE-BRUIJN : (/\ {0}) x .
rewrites: 6 in 0ms cpu (0ms real) (~ rewrites/second)
result Var: x
==========================================
rewrite in DE-BRUIJN : (/\ /\ {0}) x .
rewrites: 13 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: /\ {0}
==========================================
rewrite in DE-BRUIJN : (/\ /\ {1}) x .
rewrites: 12 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: /\ x
==========================================
rewrite in DE-BRUIJN : (/\ /\ x {1} y) x .
rewrites: 20 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: /\ x x y
==========================================
rewrite in LAMBDA : (/\ x . x) y .
rewrites: 3 in 0ms cpu (0ms real) (~ rewrites/second)
result Var: y
==========================================
rewrite in LAMBDA : (/\ x . x) (/\ x . x) .
rewrites: 3 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S K K
==========================================
rewrite in LAMBDA : (/\ f . (/\ x . f x) y) g .
rewrites: 36 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: g y
==========================================
rewrite in LAMBDA : (/\ z . z z) (/\ x . /\ y . x y) .
rewrites: 35 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S (K (S (S (K S) (S (K K) (S K K))) (S (S (K S) (K K)) (K K)))) (S
    K K)
==========================================
rewrite in CURRYING : (/\ x y z . x y z) a b .
rewrites: 152 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S (S (K a) (K b)) (S K K)
==========================================
rewrite in CURRYING : (/\ x y z . x y z) (/\ x y z . x y z) a b .
rewrites: 230 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S (S (K a) (K b)) (S K K)
==========================================
rewrite in CURRYING : (/\ x y z . (/\ x y z . x y z) y z) (/\ x y z . x y z) a
    b .
rewrites: 4467 in 4ms cpu (4ms real) (1116750 rewrites/second)
result Exp: S (S (K a) (K b)) (S K K)
==========================================
rewrite in CHURCH-BOOLEANS : and true false .
rewrites: 131 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S (S (K S) (K K)) (K K)
==========================================
rewrite in CHURCH-BOOLEANS : and (and x y) z .
rewrites: 248 in 0ms cpu (0ms real) (248248 rewrites/second)
result Exp: x y (S (S (K S) (K K)) (K K)) z (S (S (K S) (K K)) (K K))
==========================================
rewrite in CHURCH-BOOLEANS : and x (and y z) .
rewrites: 248 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: x (y z (S (S (K S) (K K)) (K K))) (S (S (K S) (K K)) (K K))
==========================================
rewrite in CHURCH-BOOLEANS : and (and true y) z .
rewrites: 203 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: y z (S (S (K S) (K K)) (K K))
==========================================
rewrite in CHURCH-BOOLEANS : and true (and y z) .
rewrites: 203 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: y z (S (S (K S) (K K)) (K K))
==========================================
rewrite in CHURCH-BOOLEANS : and (and false y) z .
rewrites: 264 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S (S (K S) (K K)) (K K)
==========================================
rewrite in CHURCH-BOOLEANS : and false (and y z) .
rewrites: 178 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S (S (K S) (K K)) (K K)
==========================================
rewrite in CHURCH-BOOLEANS : and (and false true) false t f .
rewrites: 278 in 1ms cpu (0ms real) (278000 rewrites/second)
result Var: f
==========================================
rewrite in CHURCH-BOOLEANS : and false (and true false) t f .
rewrites: 192 in 0ms cpu (0ms real) (~ rewrites/second)
result Var: f
==========================================
rewrite in DISPLAY-CHURCH-NUMERALS : display(succ #5) .
rewrites: 417 in 1ms cpu (0ms real) (417000 rewrites/second)
result NzNat: 6
==========================================
rewrite in DISPLAY-CHURCH-NUMERALS : display(succ' #5) .
rewrites: 417 in 0ms cpu (0ms real) (~ rewrites/second)
result NzNat: 6
==========================================
rewrite in DISPLAY-CHURCH-NUMERALS : display(succ (/\ x y . x)) .
rewrites: 193 in 0ms cpu (0ms real) (~ rewrites/second)
result [FindResult]: display(0, S (K #) (S K K))
==========================================
rewrite in DISPLAY-CHURCH-NUMERALS : display(succ' (/\ x y . x)) .
rewrites: 229 in 0ms cpu (0ms real) (~ rewrites/second)
result [FindResult]: display(1, S (K #) (S K K))
==========================================
rewrite in DISPLAY-CHURCH-NUMERALS : display(plus #5 #5) .
rewrites: 1360 in 1ms cpu (0ms real) (1360000 rewrites/second)
result NzNat: 10
==========================================
rewrite in DISPLAY-CHURCH-NUMERALS : display(plus #0 #5) .
rewrites: 1098 in 1ms cpu (0ms real) (1098000 rewrites/second)
result NzNat: 5
==========================================
rewrite in DISPLAY-CHURCH-NUMERALS : display(plus (succ #5) #4) .
rewrites: 1664 in 0ms cpu (1ms real) (1665665 rewrites/second)
result NzNat: 10
==========================================
rewrite in DISPLAY-CHURCH-NUMERALS : display(succ (plus #5 #4)) .
rewrites: 1677 in 1ms cpu (1ms real) (1677000 rewrites/second)
result NzNat: 10
==========================================
rewrite in DISPLAY-CHURCH-NUMERALS : display(mult #5 #5) .
rewrites: 1253 in 1ms cpu (0ms real) (1253000 rewrites/second)
result NzNat: 25
==========================================
rewrite in DISPLAY-CHURCH-NUMERALS : display(power #5 #3) .
rewrites: 3520 in 2ms cpu (1ms real) (1760000 rewrites/second)
result NzNat: 125
==========================================
rewrite in CHURCH-PAIRS : 1st (pair a b) .
rewrites: 199 in 0ms cpu (0ms real) (~ rewrites/second)
result Var: a
==========================================
rewrite in CHURCH-PAIRS : 2nd (pair a b) .
rewrites: 210 in 0ms cpu (0ms real) (~ rewrites/second)
result Var: b
==========================================
rewrite in CHURCH-PAIRS : pair (1st p) (2nd p) .
rewrites: 232 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S (S (S K K) (K (p (S (K K) (S K K))))) (K (p (S (S (K S) (K K)) (K
    K))))
==========================================
rewrite in CHURCH-PAIRS : 1st (pair (1st p) (2nd p)) .
rewrites: 255 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: p (S (K K) (S K K))
==========================================
rewrite in CHURCH-PAIRS : 1st p .
rewrites: 35 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: p (S (K K) (S K K))
==========================================
rewrite in CHURCH-PAIRS : 2nd (pair (1st p) (2nd p)) .
rewrites: 263 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: p (S (S (K S) (K K)) (K K))
==========================================
rewrite in CHURCH-PAIRS : 2nd p .
rewrites: 44 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: p (S (S (K S) (K K)) (K K))
==========================================
rewrite in CHURCH-FIBONACCI : display(fibo #4) .
rewrites: 32193 in 128ms cpu (129ms real) (249594 rewrites/second)
result NzNat: 3
==========================================
rewrite in CHURCH-FIBONACCI : display(fibo (mult #5 #2)) .
rewrites: 567887 in 3592ms cpu (3593ms real) (158077 rewrites/second)
result NzNat: 55
==========================================
rewrite in CHURCH-PREDECESSOR : display(pred #0) .
rewrites: 5807 in 1ms cpu (1ms real) (2904952 rewrites/second)
result Zero: 0
==========================================
rewrite in CHURCH-PREDECESSOR : display(pred #1) .
rewrites: 7369 in 6ms cpu (6ms real) (1052864 rewrites/second)
result Zero: 0
==========================================
rewrite in CHURCH-PREDECESSOR : display(pred #5) .
rewrites: 27958 in 95ms cpu (96ms real) (291271 rewrites/second)
result NzNat: 4
==========================================
rewrite in CHURCH-SUBTRACTION : display(sub #5 #3) .
rewrites: 493085 in 15116ms cpu (15124ms real) (32618 rewrites/second)
result NzNat: 2
==========================================
rewrite in CHURCH-SUBTRACTION : display(sub #3 #5) .
rewrites: 276698 in 12916ms cpu (12918ms real) (21422 rewrites/second)
result Zero: 0
==========================================
rewrite in CHURCH-RELATIONS : equal (mult #5 #3) (pred (power #2 #4)) t f .
>>>>>>>>>>>>>>>>>>>> KILLED IT AFTER >1h
==========================================
rewrite in CHURCH-RELATIONS : equal (mult #5 #3) (succ (power #2 #4)) t f .
>>>>>>>>>>>>>>>>>>>> KILLED IT
==========================================
rewrite in FIXED-POINT-COMBINATORS : Y-name .
rewrites: 46 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S (S (S (K S) (S (K K) (S K K))) (S (S (K S) (S (S (K S) (K K)) (K
    K))) (S (S (K S) (K K)) (K K)))) (S (S (K S) (S (K K) (S K K))) (S (S (K S)
    (S (S (K S) (K K)) (K K))) (S (S (K S) (K K)) (K K))))
==========================================
rewrite in FIXED-POINT-COMBINATORS : Y-value .
rewrites: 151 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S (S (S (K S) (S (K K) (S K K))) (S (S (K S) (S (S (K S) (S (K K) (
    K S))) (S (S (K S) (S (S (K S) (S (K K) (K S))) (S (S (K S) (S (K K) (K
    K))) (S (S (K S) (K K)) (K K))))) (S (S (K S) (S (K K) (K K))) (S (S (K S)
    (K K)) (K K)))))) (S (S (K S) (S (S (K S) (S (K K) (K S))) (S (K K) (K
    K)))) (S (K K) (K K))))) (S (S (K S) (S (K K) (S K K))) (S (S (K S) (S (S (
    K S) (S (K K) (K S))) (S (S (K S) (S (S (K S) (S (K K) (K S))) (S (S (K S)
    (S (K K) (K K))) (S (S (K S) (K K)) (K K))))) (S (S (K S) (S (K K) (K K)))
    (S (S (K S) (K K)) (K K)))))) (S (S (K S) (S (S (K S) (S (K K) (K S))) (S (
    K K) (K K)))) (S (K K) (K K)))))
==========================================
rewrite in FIXED-POINT-COMBINATORS : Y-Turing .
rewrites: 63 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S (S K K) (S (S (K (S (S (K S) (S (S (K S) (K K)) (K K))) (S (S (K
    S) (S (S (K S) (S (K K) (S K K))) (S (K K) (S K K)))) (S (S (K S) (K K)) (K
    K))))) (K (S (S (K S) (S (S (K S) (K K)) (K K))) (S (S (K S) (S (S (K S) (S
    (K K) (S K K))) (S (K K) (S K K)))) (S (S (K S) (K K)) (K K)))))) (S K K))
==========================================
rewrite in FIXED-POINT-COMBINATORS : Y-Turing-value .
rewrites: 199 in 0ms cpu (0ms real) (~ rewrites/second)
result Exp: S (S K K) (S (S (K S) (S (S (K S) (S (S (K S) (S (K K) (K (S (S (K
    S) (S (S (K S) (K K)) (K K))) (S (S (K S) (S (S (K S) (S (K K) (K S))) (S (
    S (K S) (S (S (K S) (S (K K) (K S))) (S (S (K S) (S (S (K S) (S (K K) (K
    S))) (S (S (K S) (S (K K) (K K))) (S (K K) (S K K))))) (S (S (K S) (S (K K)
    (K K))) (S (K K) (S K K)))))) (S (S (K S) (S (K K) (K K))) (S (S (K S) (K
    K)) (K K)))))) (S (S (K S) (S (S (K S) (S (K K) (K S))) (S (K K) (K K)))) (
    S (K K) (K K)))))))) (S (K K) (K (S (S (K S) (S (S (K S) (K K)) (K K))) (S
    (S (K S) (S (S (K S) (S (K K) (K S))) (S (S (K S) (S (S (K S) (S (K K) (K
    S))) (S (S (K S) (S (S (K S) (S (K K) (K S))) (S (S (K S) (S (K K) (K K)))
    (S (K K) (S K K))))) (S (S (K S) (S (K K) (K K))) (S (K K) (S K K)))))) (S
    (S (K S) (S (K K) (K K))) (S (S (K S) (K K)) (K K)))))) (S (S (K S) (S (S (
    K S) (S (K K) (K S))) (S (K K) (K K)))) (S (K K) (K K))))))))) (S (K K) (S
    K K)))) (S (S (K S) (K K)) (K K)))
==========================================
rewrite in FACTORIALS : display(factorial-name #2) .
rewrites: 510561 in 33070ms cpu (33099ms real) (15438 rewrites/second)
result NzNat: 2
==========================================
rewrite in FACTORIALS : display(factorial-value #2) .
rewrites: 511316 in 33003ms cpu (33021ms real) (15492 rewrites/second)
result NzNat: 2
==========================================
rewrite in FACTORIALS : display(factorial-Turing #2) .
rewrites: 510721 in 32976ms cpu (33010ms real) (15487 rewrites/second)
result NzNat: 2
==========================================
rewrite in FACTORIALS : display(factorial-Turing-value #2) .
rewrites: 510536 in 32826ms cpu (32833ms real) (15552 rewrites/second)
result NzNat: 2
==========================================
rewrite in FACTORIALS : display(factorial-fix #2) .
rewrites: 510479 in 33196ms cpu (33205ms real) (15377 rewrites/second)
result NzNat: 2
==========================================
rewrite in LAMBDA-WITH-BUILTINS : display((/\ x . /\ y . + x (y 7)) 5 (/\ y . *
    y 3)) .
rewrites: 83 in 0ms cpu (0ms real) (~ rewrites/second)
result NzNat: 26
==========================================
rewrite in LAMBDA-WITH-BUILTINS : display((/\ x y . if x (* (y x) x) (/\ y . y
    x)) 3 (/\ x . * 2 x)) .
rewrites: 191 in 0ms cpu (0ms real) (~ rewrites/second)
result NzNat: 18
==========================================
rewrite in LAMBDA-WITH-BUILTINS : display((/\ x y . if x (* (y x) x) (/\ y . y
    x)) 0 (/\ x . * 2 x)) .
rewrites: 180 in 0ms cpu (0ms real) (~ rewrites/second)
result [Exp,FindResult]: display(S (S K K) (K 0))
==========================================
rewrite in LAMBDA-WITH-BUILTINS : display((/\ x y . if x (* (y x) x) (/\ y . y
    x)) x (/\ x . * 2 x)) .
rewrites: 214 in 0ms cpu (0ms real) (~ rewrites/second)
result [Exp,FindResult]: display-if(display(x), * (* 2 x) x, S (S K K) (K x))
==========================================
rewrite in FACTORIALS-WITH-BUILTINS : display(factorial-name 10) .
rewrites: 3456 in 6ms cpu (6ms real) (493855 rewrites/second)
result NzNat: 3628800
==========================================
rewrite in FACTORIALS-WITH-BUILTINS : display(factorial-value 10) .
rewrites: 6079 in 14ms cpu (14ms real) (405320 rewrites/second)
result NzNat: 3628800
==========================================
rewrite in FACTORIALS-WITH-BUILTINS : display(factorial-Turing 10) .
rewrites: 3912 in 7ms cpu (7ms real) (489061 rewrites/second)
result NzNat: 3628800
==========================================
rewrite in FACTORIALS-WITH-BUILTINS : display(factorial-Turing-value 10) .
rewrites: 3056 in 3ms cpu (3ms real) (1018666 rewrites/second)
result NzNat: 3628800
==========================================
rewrite in FACTORIALS-WITH-BUILTINS : display(factorial-fix 10) .
rewrites: 3886 in 7ms cpu (8ms real) (485810 rewrites/second)
result NzNat: 3628800
Bye.
bash-3.2$ 